A closed rectangular box with a sqaure

1 answer:

6 0

Answer:

4 inches on each edge of the cube

Step-by-step explanation:

A closed box will have minimum area when it is a cube. For a volume of 64 in^3, the edge length must be ∛64 = 4 inches.

_____

Using derivatives, the base edge length can be defined as x, and the surface area as ...

S = 2x^2 + 4x(64/x^2)

This is minimized when dS/dx = 0:

dS/dx =- 4x -256/x^2 = 0

x^3 = 64

x = ∛64 = 4 . . . . . should look familiar

You might be interested in

grin007 [14]

Step-by-step explanation:

f(x) = g(x)

-3x + 4 = 2

4 - 2 = 3x

2/3 = x

5 0

3 years ago

oksian1 [2.3K]

Answer:

-30% or 30% decrease

Step-by-step explanation:

What's percentage decrease?

Percent decrease is the difference between the initial value and new value, indicating a loss of value.
The formula to find percent decrease is $\frac{NV-IV}{IV} * 100$ , where NV = new value and IV = initial value.

How do we solve this problem?

We know that the original value was $60, so that represents IV. Also, now that the price is $42, it represents NV.
Now, we plug in the values!
$\frac{42-60}{60} * 100$
$\frac{-18}{60} * 100$
$-\frac{3}{10} * 100$
$-3 * 10$
$-30$